Nano Research

, Volume 1, Issue 5, pp 395–402 | Cite as

Computational model of edge effects in graphene nanoribbon transistors

  • Pei Zhao
  • Mihir Choudhury
  • Kartik Mohanram
  • Jing Guo
Open Access
Research Article


We present a semi-analytical model incorporating the effects of edge bond relaxation, the third nearest neighbor interactions, and edge scattering in graphene nanoribbon field-effect transistors (GNRFETs) with armchair-edge GNR (AGNR) channels. Unlike carbon nanotubes (CNTs) which do not have edges, the existence of edges in the AGNRs has a significant effect on the quantum capacitance and ballistic I-V characteristics of GNRFETs. For an AGNR with an index of m=3p, the band gap decreases and the ON current increases whereas for an AGNR with an index of m=3p+1, the quantum capacitance increases and the ON current decreases. The effect of edge scattering, which reduces the ON current, is also included in the model.


Graphene nanoribbon field-effect transistor edge bond relaxation third nearest neighbor interaction edge scattering 


  1. [1]
    Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric field effect in atomically thin carbon films. Science 2004, 306, 666–669.CrossRefPubMedADSGoogle Scholar
  2. [2]
    Zhang, Y.; Tan, Y. W.; Stormer, H. L.; Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 2005, 438, 201–204.CrossRefPubMedADSGoogle Scholar
  3. [3]
    Berger, C.; Song, Z.; Li, X.; Wu, X.; Brown, N.; Naud, C.; Mayou, D.; Li, T.; Hass, J.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; de Heer, W. A. Electronic confinement and coherence in patterned epitaxial graphene. Science 2006, 312, 1191–1196.CrossRefPubMedADSGoogle Scholar
  4. [4]
    Li, X.; Wang, X.; Zhang, L.; Lee, S.; Dai, H. Chemically derived, ultrasmooth graphene nanoribbon semiconductors. Science 2008, 319, 1229–1232.CrossRefPubMedADSGoogle Scholar
  5. [5]
    Gunlycke, D.; White, C. T. Tight-binding energy dispersions of armchair-edge graphene nanostrips. Phys. Rev. B 2008, 77, 115116.Google Scholar
  6. [6]
    Son, Y. W.; Cohen, M.; Louie, S. Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 2006, 97, 216803.Google Scholar
  7. [7]
    White, C. T.; Li, J.; Gunlycke, D.; Mintmire, J. W. Hidden one-electron interactions in carbon nanotubes revealed in graphene nanostrips. Nano Lett. 2007, 7, 825–830.CrossRefPubMedADSGoogle Scholar
  8. [8]
    Sasaki, K.; Murakami, S.; Saito, R. Stabilization mechanism of edge states in graphene. Appl. Phys. Lett. 2006, 88, 113110.Google Scholar
  9. [9]
    Natori, K. Ballistic metal-oxide-semiconductor field-effect transistor. J. Appl. Phys. 1994, 76, 4879–4890.CrossRefADSGoogle Scholar
  10. [10]
    Lundstrom, M.; Guo, J. Nanoscale Transistors: Device Physics, Modeling and Simulation; Springer: New York, 2006.Google Scholar
  11. [11]
    Wong, H.-S. P.; Deng, J.; Hazeghi, A. Krishnamohan, T.; Wan, G. C. Carbon nanotube transistor circuits: Models and tools for design and performance optimization. Proc. Intl. Conf. Computer-aided Design 2006, p. 651.Google Scholar
  12. [12]
    Ouyang, Y.; Yoon, Y.; Fodor, J.; Guo, J. Comparison of performance limits for carbon nanoribbon and carbon nanotube transistors. Appl. Phys. Lett. 2006, 89, 203107.Google Scholar
  13. [13]
    Liang, G.; Neophytou, N.; Nikonov, D. E.; Lundstrom, M. Performance projections for ballistic graphene nanoribbon field-effect transistors. IEEE T. Electron Dev. 2007, 54, 677–682.CrossRefADSGoogle Scholar
  14. [14]
    Rahman, A.; Guo, J.; Datta, S.; Lundstrom, M. Theory of ballistic transistors. IEEE T. Electron Dev. 2003, 50, 1853–1864.CrossRefADSGoogle Scholar
  15. [15]
    Fiori, G.; Iannaccone, G. Simulation of graphene nanoribbon field effect transistors. IEEE Electr. Device L. 2007, 28, 760–762.CrossRefADSGoogle Scholar
  16. [16]
    Ouyang, Y.; Yoon, Y.; Guo, J. Scaling behaviors of graphene nanoribbon FETs: A three-dimensional quantum simulation study. IEEE T. Electron Dev. 2007, 54, 2223–2231.CrossRefADSGoogle Scholar
  17. [17]
    Liang, G. C.; Neophytou, N.; Lundstrom, M.; Nikonov, D. E. Ballistic graphene nanoribbon metal-oxide-semiconductor field-effect transistors: A full real-space quantum transport simulation. J. Appl. Phys. 2007, 102, 054307.Google Scholar
  18. [18]
    Guan, X.; Zhang, M.; Liu, Q.; Yu, Z. Simulation investigation of double-gate CNR-MOSFETs with a fully self-consistent NEGF and TB method. IEDM Tech. Dig. 2007, 761–764.Google Scholar
  19. [19]
    Wang, X.; Ouyang, Y.; Li, X.; Wang, H.; Guo, J.; Dai, H. Room temperature all semiconducting sub-10 nm graphene nanoribbon FETs. Phys. Rev. Lett. 2008, 100, 206803.Google Scholar
  20. [20]
    Perebeinos, V.; Tersoff, J.; Avouris, P. Electron-phonon interaction and transport in semiconducting carbon nanotubes. Phys. Rev. Lett. 2005, 94, 086802.Google Scholar
  21. [21]
    Lundstrom, M. Elementary scattering theory of the Si MOSFET. IEEE Electr. Device L. 1997, 18, 361–363.CrossRefADSGoogle Scholar
  22. [22]
    Han, M. Y.; Ozyilmaz, B.; Zhang, Y.; Kim, P. Energy bandgap engineering of graphene nanoribbons. Phys. Rev. Lett. 2007, 98, 206805.Google Scholar
  23. [23]
    Chen, Z. H.; Lin, Y. M.; Rooks, M. J.; Avouris, P. Graphene nanoribbon electronics. Physica E 2007, 40, 228–232.CrossRefADSGoogle Scholar
  24. [24]
    Fast Field Solvers. (accessed 2008).
  25. [25]
    Datta, S. Quantum Transport: Atom to Transistor; Cambridge University Press: Cambridge, 2005, pp. 170–176.MATHGoogle Scholar
  26. [26]
    Yoon, Y.; Fiori, G.; Hong, S.; Iannaccone, G.; Guo, J. Performance comparison of graphene nanoribbon FETs with Schottky contacts and doped reservoirs. IEEE T. Electron Dev. 2008, 55, 2314–2323.CrossRefADSGoogle Scholar

Copyright information

© Tsinghua University Press and Springer Berlin Heidelberg 2008

Authors and Affiliations

  • Pei Zhao
    • 1
  • Mihir Choudhury
    • 2
  • Kartik Mohanram
    • 2
  • Jing Guo
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Department of Electrical and Computer EngineeringRice UniversityHoustonUSA

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